Final answer:
The length of line segment TU is determined by setting up the equation 3x - 7 = (x + 7) + (x - 1) and solving for x. The solution x = 13 is then substituted into TU = x - 1 to find that the numerical length of TU is 12 units.
Step-by-step explanation:
The student's question involves finding the length of the line segment TU when point T is on the line segment SU and some lengths are given as algebraic expressions. Since SU is the entire segment, and ST and TU are parts of it, we can set up an equation SU = ST + TU and substitute the given expressions: 3x - 7 = (x + 7) + (x - 1). By solving this equation, we can find the value of x, which can then be used to find the numerical length of TU.
Steps to determine the numerical length of TU:
- Write the equation relating SU, ST, and TU: 3x - 7 = (x + 7) + (x - 1).
- Simplify and solve for x: 3x - 7 = 2x + 6, which leads to x = 13.
- Substitute x into the expression for TU: TU = x - 1 = 13 - 1 = 12.
Hence, the numerical length of TU is 12 units.